Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-18T10:48:25.317Z Has data issue: false hasContentIssue false
  • English
  • Français

High Speed Matrix Corrections for Quantitative X-ray Microanalysis Based on Monte Carlo Simulated K-Ratio Intensities

Published online by Cambridge University Press:  11 April 2019

John Donovan ,
Philippe Pinard Open the ORCID record for Philippe Pinard [Opens in a new window]  and
Hendrix Demers
John Donovan*
Affiliation:
University of Oregon, CAMCOR, Eugene, Oregon 97403, USA
Philippe Pinard
Affiliation:
Oxford Instruments NanoAnalysis, High Wycombe, Bucks HP12 3SE, UK
Hendrix Demers
Affiliation:
Department of Mining and Materials Engineeing, McGill University, Montréal, Québec, H3A 0C5Canada
*
*Author for correspondence: John Donovan, E-mail: [email protected]
Get access

Abstract

Due to recent advances in modeling the production of characteristic X-rays, Monte Carlo simulation of electron–solid interactions can provide improved quantitative estimates of X-ray intensities for both homogeneous and heterogeneous interaction volumes. In the case of homogeneous materials, these modeled X-ray intensities can predict with excellent accuracy, matrix corrections for arbitrary compositions, arbitrary emission lines, and electron energies. By pre-calculating these Monte Carlo X-ray intensities for pure element standards and a range of compositions of binary systems, we can derive matrix corrections for complex compositions in real-time by parameterizing these k-ratios as the so-called alpha factors. This method allows one to perform Monte Carlo-based bulk matrix corrections in seconds for arbitrary and complex compositions (with two or more elements), by combining these binary alpha factors using the so-called beta expression. We are systematically calculating X-ray intensities for 11 compositions from 1 to 99 wt% for binary pairs of all emitters and absorbers in the periodic table, for the main emission lines (Kα, Kβ, Lα, Lβ, Mα, and Mβ) at beam energies from 5 to 50 keV, using Monte Carlo calculations based on a modified PENELOPE electron-photon transport code, although any other Monte Carlo software could also be utilized. Comparison of k-ratios calculated with the proposed method and experimental k-ratios from the Pouchou and Pichoir database suggest improvements over typical φ(ρz) methods. Additional comparisons with k-ratio measurements from more complex compositions would be ideal, but our testing of the additivity of the beta equation suggests that arbitrary compositions can be handled as well, except in cases of extreme fluorescence or absorption.

Keywords

EPMAmatrix correctionsMonte CarloPenepma
Type
Software and Instrumentation
Information
Microscopy and Microanalysis , Volume 25 , Issue 3 , June 2019 , pp. 735 - 742
Copyright
Copyright © Microscopy Society of America 2019 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Albee, AL & Ray, L (1970). Correction factors for electron probe microanalysis of silicates, oxides, carbonates, phosphates, and sulfates. Analytical Chemistry, 42, 1408–1414.Google Scholar
Armstrong, JT (1988 a). Bence-Albee after 20 years: review of the accuracy of a-factor correction procedures for oxide and silicate minerals. Microbeam Analysis, Applications in Geology, 469–476.Google Scholar
Armstrong, JT (1988 b). Quantitative analysis of silicate and oxide materials: comparison of monte carlo, ZAF, and ϕ(ρz) procedures. Microbeam Anal 239–246.Google Scholar
Armstrong, JT, Carpenter, PK & Donovan, JJ (2013) CALCZAF, TRYZAF and CITZAF: The use of multi-correction-algorithm programs for estimating uncertainties and improving quantitative X-ray analysis of difficult specimens. Microsc Microanal 19 (Suppl. 2), 812–813.Google Scholar
Bastin, GF & Heijligers, HJ (2013) Quantitative electron probe microanalysis of boron, carbon, nitrogen and oxygen, ISBN 9789462282223.Google Scholar
Bence, AE & Albee, AL (1968). Empirical correction factors for the electron micro-analysis of silicates and oxides. J Geol 76, 382.Google Scholar
Donovan, JJ (2015) CalcZAF: EPMA calculation utility. https://github.com/openmicroanalysis/calczaf.Google Scholar
Gopon, P, Fournelle, J, Sobol, PE & Llovet, X (2013). Low-voltage electron-probe microanalysis of Fe–Si compounds using soft X-rays. Microscopy and Microanalysis 19, 1698–1708.Google Scholar
Horny, P (2006) Development of a quantification method for x-ray microanalysis with an electron microscope., in Department of Mining, Metals and Materials Engineering. McGill University.Google Scholar
Horny, P, Lifshin, E, Campbell, H, Gauvin, R (2010) Development of a new quantitative X-ray microanalysis method for electron microscopy. Microsc Microanal 16(6), 821–830.Google Scholar
Llovet, X & Salvat, F. (2016) PENEPMA: a Monte Carlo programme for the simulation of X-ray emission in EPMA, IOP Conference Series: Materials Science and Engineering, 109, 012009.Google Scholar
Llovet, X & Salvat, F (2017) IOP Conf Series Materials Science and Engineering 304, 012009.Google Scholar
Llovet, X, Heikinheimo, E, Galindo, AN, Merlet, C, Bello, JFA, Richter, S, Fournelle, J & van Hoek, CJG (2012 a) An inter-laboratory comparison of EPMA analysis of alloy steel at low voltage, IOP Conference Series: Material Science And Engineering 32, 012014.Google Scholar
Llovet, X, Pinard, PT, Donovan, JJ & Salvat, F (2012 b) Secondary fluorescence in electron probe microanalysis of material couples. J Appl Phys D 45, 225301.Google Scholar
Mevenkamp, N, Pinard, PT, Torrilhon, M & Richter, S (2013) Towards sub-micrometre quantification using Monte Carlo based reconstruction. European Microbeam Analysis Society, 13th European workshop, Porto, Portugal.Google Scholar
Philibert, J & Tixier, R (1968) Quantitative Electron Probe Microanalysis vol 298 ed K F J Heinrich NBS Spec. Publ. 13-33.Google Scholar
Pinard, PT, Demers, H., Hovington, P & Gauvin, R (2007) Comparison of K-ratios from Monte Carlo Codes and experimental data and evaluation of the effect of X-Ray fluorescence emission on the K-ratios, Microsc Microanal 13 (S02), 1396–1397.Google Scholar
Pinard, PT, Demers, H, Salvat, F & Gauvin, R (2009) Visualization and simulation optimization of PENELOPE through a graphical interface, Microsc Microanal 15S2, 486–487.Google Scholar
Pinard, PT, Richter, S, Demers, H & Gauvin, R (2012) evaluation of Monte Carlo Codes with experimental k-ratio of binary specimen for quantitative microanalysis. Microsc Microanal 18, 994–995.Google Scholar
Pouchou, JL & Pichoir, F (1991) Quantitative analysis of homogeneous or stratified microvolumes applying the model “PAP”. In Electron Probe Quantitation, Heinrich, KFJ, Newbury, DE (Eds), Boston, MA: Springer, pp. 31–75.Google Scholar
Shaw, HF & Albee, AL (1979) An empirical investigation into possible nonlinearities of the microprobe correction factors in the system MgO-CaO-A1203-SIO 2. In Proc. 14th Ann. Conf. Microbeam Analysis Soc (Vol. 227).Google Scholar
Teng, C, Demers, H, Brodusch, N, Waters, K & Gauvin, R (2018 a) Use of an annular silicon drift detector (SDD) versus a conventional SDD makes phase mapping a practical solution for rare earth mineral characterization. Microsc Microanal, 24, 238–248.Google Scholar
Teng, C, Demers, H & Gauvin, R (2018 b) The standard-based f-ratio quantitative x-ray microanalysis method for a field emission SEM. Microsc Microanal 24, 732–733.Google Scholar
Ziebold, TO & Ogilvie, RE (1964). An empirical method for electron microanalysis. Anal Chem 36, 322–327.Google Scholar